Find the radius of a circle, given that the center is at (3,-3) and the point (7,6) lies on the circle.

Step-by-step explanation:

The radius is the distance between the center and any point on the circle.

The formula of a distance between two points:

We have the center (3, -3) and other point on the circle (7, 6).

Substitute:

Step-by-step explanation:

if center is (3,-3), then we know the equation must look like:

(x-3)^2+(y+3)^2=r^2

Now to make sure (7,6) lies on the circle, we plug in:

(7-3)^2+(6+3)^2=16+81=97

so r= sqrt(97)

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1